Two questions am not understanding?

1) It says;

Are the foloowing subspaces?Support your answer with detials.

U1={X belong to R^n:AX=3X}

and

2)

We fix a non-zero vector d belonging to R^3, and define U3={X beloninig to R^3: proj(d)(X)=0}, where projd(x) is the projection of X onto d